Ebook: Recent Advances in Operator Theory and its Applications: The Israel Gohberg Anniversary Volume

Thisvolumecontainsaselectionofpapersinmodernoperatortheoryanditsapp- cations. Most of them are directly related to lectures presented at the Fourteenth International Workshop on Operator Theory and its Applications (IWOTA 2003) held at the University of Cagliari, Italy, in the period of June 24–27, 2003. The workshop, which was attended by 108 mathematicians – including a number of PhD and postdoctoral students – from 22 countries, presented eight special sessions on 1) control theory, 2) interpolation theory, 3) inverse scattering, 4) numerical estimates for operators, 5) numerical treatment of integral equations, 6) pseudodi?erential operators, 7) realizations and transformations of analytic functions and inde?nite inner product spaces, and 8) structured matrices. The program consisted of 19 plenary lectures of 45 minutes and 78 lectures of 30 minutes in four parallel sessions. The present volume re?ects the wide range and rich variety of topics p- sentedanddiscussedattheworkshop,bothwithinandoutsidethespecialsessions. The papers deal with inverse scattering, numerical ranges, pseudodi?erential - erators, numerical analysis, interpolation theory, multidimensional system theory, inde?nite inner products, spectral factorization, and stationary processes. SinceintheperiodthattheproceedingsofIWOTA2003werebeingprepared, Israel Gohberg, the president of the IWOTA steering committee, reached the age of 75, we decided to dedicate these proceedings to Israel Gohberg on the occasion of his 75th birthday. All of the authors of these proceedingshavejoined the editors and dedicated their papers to him as well.

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This book contains a selection of carefully refereed research papers, most of which were presented at the 14th International Workshop on Operator Theory and its Applications (IWOTA) held at Cagliari, Italy (June 24-27, 2003). The papers, many of which have been written by leading experts in the field, concern a wide variety of topics in modern operator theory and applications, with emphasis on differential operators and numerical methods. Included are papers on the structure of operators, spectral theory of differential operators, theory of pseudo-differential operators and Fourier integral operators, numerical methods for solving nonlinear integral equations, singular integral equations, and Toeplitz systems. Other main topics covered are inverse problems for canonical systems, factorization methods, metric constrained interpolation, mathematical system theory, and elements of multivariable operator theory. The book will be of interest to a wide audience of pure and applied mathematicians and engineers.

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This book contains a selection of carefully refereed research papers, most of which were presented at the 14th International Workshop on Operator Theory and its Applications (IWOTA) held at Cagliari, Italy (June 24-27, 2003). The papers, many of which have been written by leading experts in the field, concern a wide variety of topics in modern operator theory and applications, with emphasis on differential operators and numerical methods. Included are papers on the structure of operators, spectral theory of differential operators, theory of pseudo-differential operators and Fourier integral operators, numerical methods for solving nonlinear integral equations, singular integral equations, and Toeplitz systems. Other main topics covered are inverse problems for canonical systems, factorization methods, metric constrained interpolation, mathematical system theory, and elements of multivariable operator theory. The book will be of interest to a wide audience of pure and applied mathematicians and engineers.

Content:
Front Matter....Pages i-viii
Inverse Scattering with Rational Scattering Coefficients and Wave Propagation in Nonhomogeneous Media....Pages 1-20
Aluthge Transforms and the Convex Hull of the Spectrum of a Hilbert Space Operator....Pages 21-39
Maximal Nevanlinna-Pick Interpolation for Points in the Open Unit Disc....Pages 41-52
On the Numerical Solution of a Nonlinear Integral Equation of Prandtl’s Type....Pages 53-79
Fourier Integral Operators and Gelfand-Shilov Spaces....Pages 81-100
Strongly Regular J-inner Matrix-valued Functions and Inverse Problems for Canonical Systems....Pages 101-160
Regularization Processes for Real Functions and Ill-posed Toeplitz Problems....Pages 161-178
Minimal State-space Realization for a Class of nD Systems....Pages 179-194
Continuity in Weighted Besov Spaces for Pseudodifferential Operators with Non-regular Symbols....Pages 195-216
A New Proof of an Ellis-Gohberg Theorem on Orthogonal Matrix Functions Related to the Nehari Problem....Pages 217-232
Schur-type Algorithms for the Solution of Hermitian Toeplitz Systems via Factorization....Pages 233-252
Almost Pontryagin Spaces....Pages 253-271
Multivariable ?-contractions....Pages 273-298
The Singularly Continuous Spectrum and Non-Closed Invariant Subspaces....Pages 299-309
Numerical Methods for Cauchy Singular Integral Equations in Spaces of Weighted Continuous Functions....Pages 311-336
On a Gevrey-Nonsolvable Partial Differential Operator....Pages 337-356
Optimal Prediction of Generalized Stationary Processes....Pages 357-366
Symmetries of 2D Discrete-Time Linear Systems....Pages 367-382
An Algorithm for Solving Toeplitz Systems by Embedding in Infinite Systems....Pages 383-401
Fredholm Theory and Numerical Linear Algebra....Pages 403-411
Additive and Multiplicative Perturbations of Exponentially Dichotomous Operators on General Banach Spaces....Pages 413-424
Factorization of Block Triangular Matrix Functions with Off-diagonal Binomials....Pages 425-439
Closely Connected Unitary Realizations of the Solutions to the Basic Interpolation Problem for Generalized Schur Functions....Pages 441-468
Trace-Class Weyl Transforms....Pages 469-478

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This book contains a selection of carefully refereed research papers, most of which were presented at the 14th International Workshop on Operator Theory and its Applications (IWOTA) held at Cagliari, Italy (June 24-27, 2003). The papers, many of which have been written by leading experts in the field, concern a wide variety of topics in modern operator theory and applications, with emphasis on differential operators and numerical methods. Included are papers on the structure of operators, spectral theory of differential operators, theory of pseudo-differential operators and Fourier integral operators, numerical methods for solving nonlinear integral equations, singular integral equations, and Toeplitz systems. Other main topics covered are inverse problems for canonical systems, factorization methods, metric constrained interpolation, mathematical system theory, and elements of multivariable operator theory. The book will be of interest to a wide audience of pure and applied mathematicians and engineers.

Content:
Front Matter....Pages i-viii
Inverse Scattering with Rational Scattering Coefficients and Wave Propagation in Nonhomogeneous Media....Pages 1-20
Aluthge Transforms and the Convex Hull of the Spectrum of a Hilbert Space Operator....Pages 21-39
Maximal Nevanlinna-Pick Interpolation for Points in the Open Unit Disc....Pages 41-52
On the Numerical Solution of a Nonlinear Integral Equation of Prandtl’s Type....Pages 53-79
Fourier Integral Operators and Gelfand-Shilov Spaces....Pages 81-100
Strongly Regular J-inner Matrix-valued Functions and Inverse Problems for Canonical Systems....Pages 101-160
Regularization Processes for Real Functions and Ill-posed Toeplitz Problems....Pages 161-178
Minimal State-space Realization for a Class of nD Systems....Pages 179-194
Continuity in Weighted Besov Spaces for Pseudodifferential Operators with Non-regular Symbols....Pages 195-216
A New Proof of an Ellis-Gohberg Theorem on Orthogonal Matrix Functions Related to the Nehari Problem....Pages 217-232
Schur-type Algorithms for the Solution of Hermitian Toeplitz Systems via Factorization....Pages 233-252
Almost Pontryagin Spaces....Pages 253-271
Multivariable ?-contractions....Pages 273-298
The Singularly Continuous Spectrum and Non-Closed Invariant Subspaces....Pages 299-309
Numerical Methods for Cauchy Singular Integral Equations in Spaces of Weighted Continuous Functions....Pages 311-336
On a Gevrey-Nonsolvable Partial Differential Operator....Pages 337-356
Optimal Prediction of Generalized Stationary Processes....Pages 357-366
Symmetries of 2D Discrete-Time Linear Systems....Pages 367-382
An Algorithm for Solving Toeplitz Systems by Embedding in Infinite Systems....Pages 383-401
Fredholm Theory and Numerical Linear Algebra....Pages 403-411
Additive and Multiplicative Perturbations of Exponentially Dichotomous Operators on General Banach Spaces....Pages 413-424
Factorization of Block Triangular Matrix Functions with Off-diagonal Binomials....Pages 425-439
Closely Connected Unitary Realizations of the Solutions to the Basic Interpolation Problem for Generalized Schur Functions....Pages 441-468
Trace-Class Weyl Transforms....Pages 469-478
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